Daniel K. Inouye, Senator for Hawaii(WASHINGTON) -- The late Sen. Daniel Inouye, D-Hawaii, will lie in state in the U.S. Capitol Rotunda, a source with knowledge of plans tells ABC News. It is one of the highest honors Congress can bestow on an individual.

There is no date set for this rare honor yet, Hill sources say.

On Tuesday, one day after his passing, Sen. Inouye’s desk in the U.S. Senate was draped in a black cloth, Hawaiian ceremonial kukui nut beads and adorned with a vase full of white roses in tribute.

The day started with a moment of silence for the senator and the Senate Chaplain Barry Black prayed for the “beauty of his well-lived life.”

That life and remembrances – from the serious to the lighthearted – from senators on both sides of the political aisle monopolized most of the Senate floor time Tuesday. Sen. Dick Durbin, D-Ill., spoke about how Inouye never seemed to break a sweat, literally. When others at an extremely hot outside event were dripping in sweat, Inouye was cool as a cucumber, Durbin recalled.

“He says, you know, ‘the Asian religions are very important in my life, and they believe that mind over matter can achieve great things, and can I visualize myself sitting in a deep freeze now. I’m not hot at all.’ I thought this man is amazing in so many different ways what he has done with his life.”

Many described the late senator as humble, some noting that he didn’t even hang pictures of himself nor his accomplishments over the years in his Senate office – a rarity among Senate personalities and egos.

“He was exactly the opposite of all the caricature pictures people have of Congress today, and particularly about the rabid partisanship and personal incivility,” Sen. Lieberman, I-Conn., said, “Dan was a great gentleman, and the most civil of people, the kindest and most decent of people.”

Senate Minority Leader McConnell, R-Ky., said he was “never drawn to fanfare,” which always made him a “different kind of senator.”

“Dan’s quiet demeanor and strict adherence to an older code of honor and professionalism made him a stranger to controversy throughout his many decades in public office,” McConnell said, “He was the kind of man, the kind of public servant, in other words, that America has always been grateful to have. Especially in her darkest hours, men who lead by example and expect nothing in return.”

Sen. Orrin Hatch, R-Utah., praised Inouye’s career before he even came to Congress, calling his military service “the stuff of legend here in the Senate and throughout the country.”

Inouye was a decorated war hero who lost his arm in battle. In 2000 Inouye was awarded the Medal of Honor for his service in Europe in World War II.

“While he and I often found ourselves on different sides when it came to issues, I always knew him to be a man of principle and decency,” Hatch said, “and I never doubted his commitment to the people of his state and to doing what he believed was right.”

“It’s with a heavy heart that those of us who love Senator Inouye say aloha to a great man, a legend of the Senate and his final dying word, Mr. President, was ‘aloha.’ It didn’t mean goodbye. It meant 'I love you.' And Senator Inouye, I love you.”

Inouye was 88 years old when he died. He had been in office since Hawaii became a state in 1959. He became Hawaii’s senator in 1962, three years after the state joined the United States. He was the longest-serving sitting senator and the second-longest serving senator in U.S. history.